This is something I've thought about frequently, and I completely agree. The "purpose" of my existence would be maintained, so why would I care which one you choose?
We all do this without thought on a daily basis with files on our filesystem. A particular document encodes a set of information; if we duplicate that document, we now have two identical copies of the same information. By the original author's argument, they are unique and distinct, because they occupy different blocks on our storage medium! But common sense makes it clear that which one we delete doesn't matter, because they serve the same purpose - provided that we preserve at least one copy.
(To those that argue that the file system metaphor is flawed, because consciousness is "different" or "special" in some way, I reference the inverse of Clarke's Third Law: Any sufficiently understood magic is indistinguishable from technology.)
Now, if those documents continue to evolve and change over time, such that they no longer match, now you are left with a version control problem, and one that seems to be nigh-impossible to solve with a consciousness. In my opinion, this is a situation worth avoiding if we can, as it becomes very sticky very quickly, since the uniqueness of the experiences produces an infinite gradient that makes deciding on an appropriate cutoff of termination very difficult.
As for the continuity of thought, we certainly don't see falling asleep at the end of the day as the "death" of our current consciousness, or waking up in the morning as the "birth" of our new consciousness, despite the (perceived) discontinuity. So why would your source or target self perceive it that way?
Fortunately, regardless of how you feel about the whole "continuity of thought" argument, the solution is very simple - users would simply not be required to make use of these new products/services. Don't want to get faxed to Mars? No problem! Users are not currently required to make copies of files, or transmit files, or make backups of files, after all.
Anyway, that was longer than I had intended. Hopefully someone finds that somewhat interesting, although I suppose it's really all moot anyway until we're even remotely close to the technology required to implement this.